The correlation measure of order k is an important measure of pseudorandomness for binary sequences. This measure tries to look for dependence between several shifted versions of a sequence. We study the relation between the correlation measure of order k and two other pseudorandom measures: the Nth linear complexity and the Nth maximum order complexity. We simplify and improve several state-of-the-art lower bounds for these two measures using the Hamming bound as well as weaker bounds derived from it.

中文翻译：

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二元序列族的相关度量、线性复杂度和最大阶复杂度

k阶相关性度量是二进制序列伪随机性的重要度量。该度量试图寻找序列的多个移位版本之间的依赖关系。我们研究了k阶相关度量与其他两个伪随机度量之间的关系：第N个线性复杂度和第N个最大阶复杂度。我们使用汉明界以及从中派生的较弱的界来简化和改进这两个度量的几个最先进的下界。